Question: $a_n=\dfrac{(-5)^n}{(n+3)8^{n+1}}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$
Solution: $\lim_{n\to\infty}\left| \,\frac{{{a}_{n+1}}}{{{a}_{n}}}\, \right|=\dfrac{5}{8}$ Since the limit, $\dfrac{5}{8}$, is less than $1$, the ratio test tells us that the series converges.